Classroom environments that foster a sense of community that allows students to express their mathematical ideas—together with norms that expect students to communicate their mathematical thinking to their peers and teacher, both orally and in writing, using the language of mathematics—positively affect participation and engagement among all students.

Principles to Action, NCTM

The beginning of the school year offers teachers and students a fresh start full of exciting possibilities. From the first day of class, as we begin to learn about each of the students in front of us, we have the opportunity to set the stage for how learning math will look, sound, and feel throughout the year. We also begin to foster the attitudes and beliefs that are important in shaping a mathematical classroom community in which each and every student is positioned as a capable learner and doer of mathematics, truly believes their voice is valued and heard, and understands that we learn math by doing deep and meaningful mathematics together. Building this classroom community requires a purposeful process that takes time and careful attention.

To build this community, it is first important to be mindful of who is involved in the process. While it may be fast and easy to simply tell students how they will engage in math this year by offering a given set of rules or norms, it completely removes student ownership in their own learning. It is also a missed opportunity to engage students in reflecting on the things they need to feel safe and successful in mathematics. To be invested in a classroom community, students should be active participants in identifying what it means for them to do math and the collective norms that allow each and every one of them the opportunity to do so.

Student-generated norms offer guidance and continuous reminders to students as to how they can work collaboratively and productively as individuals as well as in groups. Even with the best of intentions, however, all too often we establish norms at the beginning of the year only to struggle to maintain them. Creating norms within the context of building a mathematical community moves the norms from just a poster on the wall to a living, breathing culture in the classroom.

There are two important considerations when planning the student experiences through which to establish norms:

The experiences should be reflective of how learning math will look, sound, and feel all year.

The experiences should be connected to convey the message that learning math is a coherent journey.

If we want students to have access to, and engage in, deep and meaningful mathematics, their opportunities to do mathematics should be connected. A series of connected experiences that encourage mathematical discussions, collaborative work, and engagement in the Mathematical Practices not only create a mathematical classroom culture, but also give students a coherent picture of what it means to learn math. Through these experiences, the established norms are continuously reinforced.

The first two weeks of class are often dedicated to giving students exciting math problems and establishing norms. While this is great for engaging students in mathematics, these activities are typically disconnected, isolated tasks that then create the need for the teacher to establish new routines and lesson structures when starting their first curriculum unit. These additional tasks take time and can add extra days into an already full year of learning, forcing teachers to make decisions about which content to cut later in the year because of pacing issues.

From the beginning of Unit 1 in the IM 6–8 Math curriculum, the problem-based lesson structure engages students in collaborative, connected mathematical experiences. Through warm-ups such as “Which One Doesn’t Belong,” “Notice and Wonder,” and “Number Talks,” and classroom activities that include card sorts and interactive Geogebra applets, the norms are intrinsic to the daily function of the mathematics classroom throughout the year.

Linked below is a process to start building a mathematical classroom community during the first week of school in Unit 1 of the IM 6–8 Math curriculum. In preparation for this work, we recommend teachers read the “What Is a Problem-based Curriculum?” section of the curriculum course guide to gain insight into the ways students actively participate in the learning throughout a lesson.

Here are some ideas to help maintain your mathematical community norms throughout the year:

As the teacher, be a daily example of what it looks like to do math and be mindful of the community norms.

After the first week, be sure to revisit the “Mathematical Community” ideas and ask for revisions at least once a week. It is easy to focus solely on the math students are doing, but by revisiting this list it shows students that you value the mathematical community as much as you value the math.

To ensure this is a working and growing collection of ideas, make Post-its available to students and ask them to make suggestions or show evidence of either doing math or norms they experienced.

Before launching activities that require a lot of group interaction, remind students of their mathematical community ideas so the ideas are at the forefront of their work.

As students work during a lesson, occasionally monitor for evidence of their mathematical community in addition to the math. During the synthesis, highlight the actions and norms you saw being attended to during the lesson.

If time allows, periodically ask students to be more metacognitive about the norms by asking them which norms they think are the most difficult to follow, and why.

Organizational tip for the classroom: In the FB group, Lindsey K. posted, “I’m moving from elementary to middle school. I’ve always done collaborative norms and posted them. How do you do that for multiple classes? I was thinking of doing each class and then synthesizing all 5 on one anchor chart. Any other ideas?”

I thought this was a great question and one that many teachers face with limited wall space. I taught three 5th grade math classes and kept a separate piece of chart paper for each class because they were uniquely different. I also had an abnormally long room with a huge, empty wall that made it easy to do! If you are short on wall space, I think consolidating the class norms to one poster is a way to save space. And then, to value each classes’ differences, you could make a 5×8 index card or copy of the norms on card stock to tape to the front of their workbooks or math journals.

Next Step

If you use this process, we would love to see your students’ ideas and hear about your experience. You can share your pictures, blog post links, and reflections in the comments section below, or on Twitter using our #LearnWithIM hashtag and tagging @IllustrateMath!

The lessons referenced are from the Illustrative Mathematics 6-8 Curriculum. It’s currently available through Open Up Resources (http://im.openupresources.org) and LearnZillion (https://learnzillion.com/p/illustrative-mathematics/). The curriculum is available to access for free via Open Up. Register for a (free!) teacher account to access additional materials, like pre- and end-unit assessments. Check it out! 🙂

Jenna, I’m still having a hard time finding the lesson plan that the “Building a Mathematical Classroom Community” blog is referring to. Can you possibly send me a link? I’m putting together a few orientation lessons and I think this is an awesome resource, but I can only get the overview here, https://drive.google.com/file/d/1nYBD0iUpFavjLMHDgM2TTWwTY-rIrhM3/view. Thanks!